Domain decomposition for nonlinear parabolic problems in a variational framework

Monika Eisenmann (TU Berlin), Eskil Hansen

Nonlinear parabolic equations are frequently encountered in applications, but in practice constructing an approximation for these problems yields a large scale computational system. In order to obtain an efficient algorithm for the numerical approximation, it can be useful to apply a scheme that consists of a number of independently solvable subproblems to make use of a parallel computing hardware.

In our work, we introduce a general framework of non-autonomous, inhomogeneous evolution equations in a variational setting and show convergence of an operator splitting scheme via a time discretization. This approach covers a fairly general class of parabolic differential equations. We exemplify the usage to a \(p\)-Laplacian type problem with a possibly time depending domain decomposition.